Sentence examples for the large cardinal from inspiring English sources

Landis had hoped that the large Cardinal farm system would become economically unfeasible; when it proved successful for the Cardinals, he had tolerated it for several years and was in a poor position to abolish it.

Otherwise the large cardinal is large.

The critical point is (typically) the large cardinal associated with the embedding.

The weaker of the large cardinal principles are supported by intrinsic evidence (see section 3.1).

The stronger of the large cardinal principles hitherto only enjoy extrinsic support.

One such class of principles is constituted by the large cardinal axioms.

From studies on infinitary logics, William Hanf, an American logician, was able to define certain cardinals, some of which have been studied in connection with the large cardinals in set theory.

The large cardinals considered thus far (including κ are known as small large cardinals.

Both the largest cardinal and the largest ordinal arise from considering the very largest collections (such as the universe V).

Consideration of the largest ordinal number gave rise to the Burali-Forti paradox, and consideration of the largest cardinal number gave rise to the Cantor paradox.

The interesting thing about these large cardinal hypotheses is that for n > 0 they are inconsistent with AC (by a result of Kunen).